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Practical GDT Designs

Now the fun bit - practical transformer designs!

 

Leakage Inductance Calculation

To reduce leakage inductance, we must increase the coupling between the windings. It's that simple.

Well OK, it's not that simple. We'll start by defining the formula for interwinding coupling as

k = SQRT [ 1 - ( L-leak / L-mag ) ]

where:
k = coupling coefficient (no units)
L-leak = leakage inductance (Henries)
L-mag = magnetising inductance (Henries)
SQRT [ x ] = square root of contents of brackets

Magnetising inductance remains constant for x number of turns, so to decrease the leakage inductance we need to increase the coupling between windings.

To get maximum coupling, the windings would need to occupy the same physical space as each other for a coupling of 1 (unity), which is clearly not possible. The next best thing is to get them as close as possible. Various suggestions have been made as to the best way of doing this, but there didn't seem to be any data to back it all up. So I decided to do my own measurements to try and find the best winding technique for GDTs with the aim of minimising leakage inductance.

 

Design Experiments

I had some Epcos N87 ferrite toroids from a previous project that I thought I'd use for this. They aren't recommended for GDT design as they have a poor AL but they were convenient. Some basic rules were set for these experiments

  • Cores used were Epcos B64290-L626-X87
  • Wire was 0.4mm Grade 2 ECW (0.45mm outer diameter)
  • Each winding consisted of 15 turns
  • The turns ratio for each transformer was 1:1:1 (three equal windings)
  • Each winding was terminated with 15mm of wire to simulate the typical connection lengths involved
  • Leakage inductance was obtained by measuring the windings to find the one with the lowest inductance. This winding was then measured with the other two windings shorted

Three types of winding style were tried first to ascertain the best for reducing leakage inductance - delta, sectional and circumferential. These were first wound with overlaid strands of wire and pictures of the cores are shown below

    

Delta, Sectional and Circumferential wound GDTs

Circumferential was found to have the lowest leakage so this technique was used with tri-filar wire and screened wire.

The tri-filar was twisted together using a vice to grip one end of the wire with the other end in the chuck of a hand drill. The hand drill was turned until about 2 turns per inch was achieved on the wire. When making filar wire and you have finished twisting it, run the drill backwards to untwist a few turns before releasing the tension as it stops the wire from knotting when tension is released.

The screened wire core was made of a bi-filar wound string with about 2 turns per inch with each wire forming one of the secondaries. The primary screen was made from sections of tinned copper braid about 3" long that were soldered together to form a continuous screen. With tinned copper braid, poking a screwdriver down the end pushes the strands out to form a tube that can be slid over the wires used as the core. You are limited to the maximum length by how long your screwdriver is but these sections can be soldered together to form one long screen around the secondary wires. The lot was insulated with black electrical insulating tape.

Pictures of these two cores are shown below

  

Trifilar and Screened GDTs

Leakage inductance and winding inductance were measured at frequencies of 100kHz, 200kHz and 300kHz with the mean result being taken of the three. The results of the measurements are shown in the below table:

Wire Type Winding Type Leakage Inductance
(average, uH)
Winding Inductance
(average, uH)
Coupling Factor
(k, no units)
Overlaid Delta 10.58 457.71 0.988379
Overlaid Sectional 0.46 453.2 0.999456
Overlaid Circumferential 0.17 431.88 0.999803
Tri-Filar Circumferential 0.159 487.16 0.999837
Screened Circumferential 0.08 451.1 0.999905

As can be seen, the delta winding technique produces a very high leakage inductance due to the large physical separation of the windings, whereas the tri-filar and screened wires with the close physical proximity have relatively low leakage inductance, the screened coming in at just 80nH.

For GDT applications, using the screened wire technique gives the best performance, but with filar wound also giving acceptable results.

In an attempt to find out if the tightness of the winding made any significant difference to the leakage inductance, two GDTs were wound to try and measure the effect. The cores and principles used were exactly the same as used in the previous experiment but this time with only two windings of 15 turns forming a 1:1 transformer.

Difference between loose wound and tight wound coils in terms of the leakage inductance is minimal, measuring only 1uH difference between the two. Average leakage inductances measured were

  • Loose wound = 13.5uH
  • Tight wound = 12uH

There appears to be some benefit in using tight wound coils on the core, but leakage primarily depends on coupling between windings. Using CAT-5 twisted pair cable has become popular for making GDTs with good results. However the outer insulation will space the wires away from the core, increasing the leakage - better to remove the outer sheath.